This method is disclosed in “Calibration of projector lens distortions for quantitative high-resolution TEM”, F. Hue et al., Microsc. Microanal. 11 (supplement 2), 2005, pages 552-553, (DOI:10.1017/S143192760551081X), and is used to correct the distortions introduced by the projection system of a Transmission Electron Microscope (TEM).
In a TEM an object, also referred to as a sample, is irradiated with a beam of electrons, the electrons having an energy of e.g. between 50 keV and 400 keV. Some of the electrons are transmitted through the sample, and these electrons are focused on the image plane to form an enlarged image of the sample. The imaging of the sample on the image plane is realized with a projection system, that can be set to a configurable magnification of e.g. between 103 and 106 times. Typically a detector, such as a fluorescent screen or a CCD camera, is placed in the image plane, whereby the image is detected.
As known to the person skilled in the art a projection system not only forms an image of the sample to the image plane, but also introduces aberrations and distortions. In this context aberrations are the errors resulting in a point to be imaged as a blur, and distortions are those errors that result in a warp of the image.
Distortions of the image may limit the performance of e.g. a TEM. Two examples where distortions are likely to limit the performance of a TEM are tomography and strain analysis.
For the construction of a 3D representation of a sample by tomography a large number of images, typically between 50 and 100 images, are made. Each image is acquired at a slightly different orientation (tilt) of the sample. By combining these images a 3D reconstruction can be formed. When the images are warped, due to distortions, the location of a feature in the sample with respect to a reference point in the sample is mis-represented. As in some images the feature may be in the centre of the image, while in other images the feature may be removed from the centre, the displacement is not constant, resulting in a blurring of the feature in the 3D reconstruction. This is aggravated by the fact that the magnification used in tomography is often relatively low, resulting in relative large distortions due to the large beam diameters in the particle-optical lenses and other particle-optical elements. Therefore in tomography distortion may limit the resolution in the 3D representation.
In strain analysis the warp of the lattice in a crystallographic sample is determined. This warp may be the result of strain, and therefore determining the warp is a manner to determine the strain in the crystal. Obviously, if the image already shows warp for an unstrained crystal, this results in errors in the strain determined when imaging strained crystals.
The aforementioned publication discloses that a sample in the form of a perfect crystal of silicon is inserted in a TEM. The location dependent displacements of the image of this perfect object are measured. It is found that the magnification over the field of view may vary as much as 5%, and that local rotation may be 2 degrees. The publication proposes to map the local displacements in a displacement field and therewith correct experimental images by displacing the pixels in the image, thus forming a modified image in which the distortion is at least partially corrected. It is found that in this way the local magnification error was reduced from its original 5% to 0.1% and the local rotation error was reduced from its initial 2 degrees to 0.1 degrees.
The publication further mentions that the projector lens distortions are quite stable over a time period of at least four years.
A disadvantage of the aforementioned method is that it demands that every image is processed to eliminate the distortions. Especially when processing a large number of images, such as used in tomography, this may limit throughput. A further disadvantage is that the displacement of the pixels in the image may result in artefacts.